Ultrasonic Attenuation in the Critical Region

The interaction of forced sound waves with critical density fluctuations is discussed quantitatively. The nonlinear equations of motion are analyzed to distinguish three contributions to the instantaneous density and temperature variation: (1) the spontaneous fluctuations that are defined as the solution to an initial value problem, (2) the macroscopically observed sound wave which oscillates with harmonic time dependence, and (3) the result of an interaction between (1) and (2). The three contributions satisfy three equations, which are discussed separately. A completely general combination of these equations to compute ultrasonic absorption and attenuation is avoided, as the requisite thermodynamic and transport coefficients are inadequately known. Because, however, a thermal relaxation mechanism has previously been treated on the basis of an oversimplified multiphase picture of spontaneous fluctuations, the present calculations are carried to completion on the assumption that only the local heat capacity is affected by the density fluctuations. The sound wave together with the fluctuating heat capacity produce temperature fluctuations, whose relaxation is the source of the absorption.

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